In many applications, it is highly desirable to make the output function of a particular circuit or system have a linear relationship with the input function of the circuit. For example, one can make a circuit or device that produces a capacitance whose value depends on an input voltage. In this case, it is desirable that the capacitance value behaves linearly with the input voltage. Another example relates to phase-locked loop (PLL) circuits which contain a voltage controlled oscillator (VCO) whose output frequency is a function of an input control voltage. In such circuits, it is also desirable that the output frequency behave linearly with respect to the input control voltage.
There are many known techniques for linearizing the input/output response of VCOs in PLL circuits. Such techniques typically utilize circuit methods which can be very complex. Other techniques divide the frequency range to several ranges and employ different circuit and computational techniques to linearize each frequency range.
It is also known to utilize gate tunneling current with gate voltages less than 3V (volts) in devices with ultra-thin gate oxides, i.e., those which have gate oxide thickness less than about 4.5 nm. The gate current (Ig) can be expressed as a power function of the gate voltage (Vg) as follows:Ig=C1×VgC2   (1)
FIG. 1 graphically depicts the relationship between parameter C1 in amps per centimeter squared (AMP/cm2) versus oxide thickness at 27 C (27 degrees Celsius).
FIG. 2 graphically depicts the relationship between parameter C2 versus oxide thickness. As is apparent from FIGS. 1 and 2, parameters C1 and C2 are functions of gate voltage and can be written as functions of oxide thickness (TOX). The range of TOX employed here is 3.5 nm to 1.2 nm. This range is selected as a practical case for the tunneling current as function of the gate voltage. The parameters C1 and C2 could be represented as follows:C1=4.8385×108×Exp[−1.301×TOX]  (2)C2=1.0611+[1.5863×TOX]  (3)The range of C2 corresponds to the TOX range, is from about 3.0 to about 6.7, and is a wide range.
The gate voltage Vg can be expressed as a function of Ig as follows:Vg=A1×IgA2   (4)where:A1=(1/C1)(1/C2)   (5)and,A2=1/C2.   (6)
There exists a need in the art for a better technique and an associated circuit through which the relationship between the output and input functions can be transformed into a linear one.